This paper is intended to demonstrate how to apply an inversion method to one of the observed solar active regions (ARs) generally having complex magnetic structure. The method was developed in our previous work for solving an inverse problem to derive physical properties of a subsurface magnetic field from surface magnetic field evolution. We handled two key issues in the application of the method to the observed AR, one of which is to reconstruct three-dimensional magnetic structure of the AR, while the other is to select a single magnetic flux tube responsible for an X-class flare observed in this AR by isolating closed magnetic-loop structure from the reconstructed AR structure. The isolation of the loop structure is essential for a proper evaluation of unsigned magnetic flux and relative magnetic helicity, which are used to solve the inverse problem. By refining data of the so-called force-free α, we also derived the principal field line representing the axis of the selected flux tube in the AR, which could contribute to a quantitative classification of ARs having full of variety in size, magnetic field strength, and magnetic field configuration.

Introduction
Data Analysis
    Observed Data
    Reconstruction of Three-Dimensional (3D) Force-Free Magnetic Structure
    Selection of Single Flux Tube
    Refinement of Force-Free α Data
Results
Summary & Discussion
Acknowledgments
References

• Tetsuya Magara(Department of Astronomy and Space Science, Kyung Hee University, Yongin-si, Gyeonggi-do 17104, Republic of Korea, School of Space Research, Kyung Hee University, Yongin-si, Gyeonggi-do 17104, Republic of Korea) Corresponding author
• Sibaek Yi(School of Space Research, Kyung Hee University, Yongin-si, Gyeonggi-do 17104, Republic of Korea)
• Yeonwoo Jang(School of Space Research, Kyung Hee University, Yongin-si, Gyeonggi-do 17104, Republic of Korea)
• Donghui Son(School of Space Research, Kyung Hee University, Yongin-si, Gyeonggi-do 17104, Republic of Korea)